24324329479508100
24,324,329,479,508,100 is an even composite number composed of six prime numbers multiplied together.
What does the number 24324329479508100 look like?
This visualization shows the relationship between its 6 prime factors (large circles) and 2025 divisors.
24324329479508100 is an even composite number. It is composed of six distinct prime numbers multiplied together. It has a total of two thousand and twenty-five divisors.
Prime factorization of 24324329479508100:
22 × 32 × 52 × 74 × 172 × 794
(2 × 2 × 3 × 3 × 5 × 5 × 7 × 7 × 7 × 7 × 17 × 17 × 79 × 79 × 79 × 79)See below for interesting mathematical facts about the number 24324329479508100 from the Numbermatics database.
Names of 24324329479508100
- Cardinal: 24324329479508100 can be written as Twenty-four quadrillion, three hundred twenty-four trillion, three hundred twenty-nine billion, four hundred seventy-nine million, five hundred eight thousand, one hundred.
Scientific notation
- Scientific notation: 2.43243294795081 × 1016
Factors of 24324329479508100
Divisors of 24324329479508100
- Number of divisors d(n): 2025
-
Complete list of divisors:
1 2 3 4 5 6 7 9 10 12 14 15 17 18 20 21 25 28 30 34 35 36 42 45 49 50 51 60 63 68 70 75 79 84 85 90 98 100 102 105 119 126 140 147 150 153 158 170 175 180 196 204 210 225 237 238 245 252 255 289 294 300 306 315 316 340 343 350 357 395 420 425 441 450 474 476 490 510 525 553 578 588 595 612 630 686 700 711 714 735 765 790 833 850 867 882 900 948 980 1020 1029 1050 1071 1106 1156 1185 1190 1225 1260 1275 1343 1372 1422 1428 1445 1470 1530 1575 1580 1659 1666 1700 1715 1734 1764 1785 1975 2023 2058 2100 2142 2205 2212 2370 2380 2401 2450 2499 2550 2601 2686 2765 2844 2890 2940 2975 3060 3087 3150 3318 3332 3430 3468 3555 3570 3675 3825 3871 3950 4029 4046 4116 4165 4284 4335 4410 4740 4802 4900 4977 4998 5100 5145 5202 5355 5372 5530 5780 5831 5925 5950 6069 6174 6241 6300 6636 6715 6860 7110 7140 7203 7225 7350 7497 7650 7742 7900 8058 8092 8295 8330 8575 8670 8820 8925 9401 9604 9954 9996 10115 10290 10404 10710 11025 11060 11613 11662 11850 11900 12005 12087 12138 12348 12482 12495 13005 13430 13825 14161 14220 14406 14450 14700 14994 15300 15435 15484 16116 16590 16660 17150 17340 17493 17775 17850 18207 18723 18802 19355 19908 20145 20230 20580 20825 21420 21609 21675 22050 22831 23226 23324 23700 24010 24174 24276 24885 24964 24990 25725 26010 26775 26860 27097 27650 28203 28322 28812 28900 29155 29988 30345 30870 31205 33180 33575 34300 34839 34986 35550 35700 36015 36414 37446 37485 37604 38710 40290 40460 40817 41475 41650 42483 43218 43350 43687 44100 45662 46452 47005 48020 48348 49770 49980 50575 51450 52020 52479 53550 54194 55300 56169 56406 56644 58065 58310 60025 60435 60690 61740 62410 62475 65025 65807 67150 68493 69678 69972 70805 71100 72030 72828 74892 74970 77175 77420 80580 81291 81634 82950 83300 84609 84966 86436 86700 87374 87465 91035 91324 93615 94010 96775 99127 99540 100725 101150 102900 104958 106097 107100 108045 108388 112338 112812 114155 116130 116620 120050 120870 121380 122451 124425 124820 124950 127449 130050 131061 131614 134300 135485 136986 139356 141015 141610 144060 145775 149940 151725 154350 156025 159817 162582 163268 165900 169218 169932 174195 174748 174930 180075 182070 187230 187425 188020 189679 193550 197421 198254 201450 202300 204085 205479 209916 212194 212415 216090 218435 224676 228310 232260 235025 240100 241740 243873 244902 248850 249900 254898 260100 262122 262395 263228 270970 273972 280845 282030 283220 290325 291550 297381 302175 303450 305809 308700 312050 318291 319634 325164 329035 338436 342465 348390 349860 354025 360150 364140 367353 374460 374850 379358 387100 393183 394842 396508 402900 406455 408170 410958 423045 424388 424830 432180 436870 437325 455175 456620 460649 468075 470050 479451 487746 489804 493039 495635 497700 509796 524244 524790 530485 540225 541940 561690 564060 569037 570775 580650 583100 592263 594762 604350 606900 611618 612255 624100 636582 637245 639268 655305 658070 677425 684930 693889 696780 705075 708050 720300 734706 742679 749700 758716 786366 789684 799085 812910 816340 821916 846090 849660 870975 873740 874650 892143 910350 917427 921298 936150 940100 948395 954873 958902 975492 986078 987105 991270 1020425 1027395 1049580 1060970 1062075 1080450 1092175 1118719 1123380 1138074 1141550 1161300 1184526 1189524 1208700 1219365 1223236 1224510 1273164 1274490 1310610 1311975 1316140 1354850 1369860 1381947 1387778 1404225 1410150 1416100 1438353 1469412 1479117 1485358 1486905 1529045 1572732 1591455 1598170 1625820 1645175 1692180 1707111 1712325 1741950 1749300 1784286 1803649 1820700 1834854 1836765 1842596 1872300 1896790 1909746 1917804 1965915 1972156 1974210 1982540 2032275 2040850 2054790 2081667 2115225 2121940 2124150 2140663 2160900 2184350 2228037 2237438 2276148 2283100 2303245 2369052 2397255 2438730 2449020 2465195 2478175 2548980 2621220 2623950 2652425 2709700 2752281 2763894 2775556 2808450 2820300 2845185 2876706 2958234 2961315 2970716 2973810 3058090 3061275 3182910 3186225 3196340 3224543 3276525 3290350 3356157 3414222 3424650 3451273 3469445 3483900 3568572 3607298 3669708 3673530 3713395 3793580 3819492 3931830 3948420 3995425 4064550 4081700 4109580 4145841 4163334 4230450 4248300 4281326 4368700 4437351 4456074 4460715 4474876 4587135 4606490 4741975 4774365 4794510 4877460 4930390 4935525 4956350 5136975 5198753 5247900 5304850 5410947 5504562 5527788 5593595 5616900 5690370 5753412 5916468 5922630 5947620 6096825 6116180 6122550 6245001 6365820 6372450 6421989 6449086 6553050 6580700 6684111 6712314 6828444 6849300 6902546 6909735 6938890 7191765 7214596 7347060 7395585 7426790 7434525 7645225 7831033 7863660 7957275 7990850 8129100 8291682 8326668 8381663 8460900 8535555 8562652 8874702 8912148 8921430 9018245 9174270 9183825 9212980 9483950 9548730 9589020 9673629 9829575 9860780 9871050 9912700 10068471 10273950 10353819 10397506 10408335 10609700 10703315 10821894 11009124 11140185 11187190 11380740 11516225 11845260 11986275 12193650 12245100 12325975 12490002 12625543 12744900 12843978 12898172 13106100 13368222 13424628 13761405 13805092 13819470 13877780 14225925 14383530 14791170 14806575 14853580 14869050 14984641 15290450 15596259 15662066 15914550 15981700 16122715 16232841 16583364 16763326 16780785 17071110 17256365 17347225 17749404 17842860 18036490 18348540 18367650 18566975 18967900 19097460 19265967 19347258 19659150 19742100 20136942 20547900 20707638 20729205 20795012 20816670 21406630 21643788 22186755 22280370 22303575 22374380 22935675 23032450 23493099 23871825 23972550 24158911 24387300 24651950 24980004 25144989 25251086 25687956 25993765 26736444 27054735 27522810 27638940 27967975 28451850 28767060 29020887 29582340 29613150 29738100 29969282 30580900 31061457 31192518 31225005 31324132 31829100 32109945 32245430 32465682 33420555 33526652 33561570 34142220 34512730 34548675 34694450 35958825 36072980 36391271 36735300 36977925 37133950 37876629 38531934 38694516 38950081 39155165 39318300 40273884 41415276 41458410 41633340 41908315 42677775 42813260 44373510 44560740 44607150 44953923 45091225 45871350 46064900 46788777 46986198 47743650 47945100 48317822 48368145 49303900 50289978 50342355 50502172 51769095 51987530 52041675 53516575 54109470 54817231 55045620 55700925 55935950 56903700 58041774 58671641 59226300 59938564 62122914 62385036 62450010 63127715 64219890 64490860 64931364 66841110 67123140 68807025 69025460 69097350 69388900 70479297 71917650 72476733 72782542 73955850 74267900 74923205 75434967 75753258 77063868 77900162 77981295 78310330 80613575 81164205 82916820 83816630 83903925 85355550 86281825 88378801 88747020 89214300 89907846 90182450 91742700 93577554 93972396 95487300 96329835 96635644 96736290 100579956 100684710 103538190 103646025 103975060 104083350 107033150 108218940 109173813 109634462 110933775 111401850 111871900 113629887 116083548 116850243 117343282 117465495 120794555 124245828 124900020 125724945 126255430 128439780 129968825 133682220 134861769 135273675 137614050 138194700 140958594 142488271 143835300 144953466 145104435 145565084 147911700 149846410 150869934 151506516 155307285 155800324 155962590 156125025 156620660 160549725 161227150 162328410 164451693 167102775 167633260 167807850 169112377 170711100 172563650 176014923 176757602 179815692 180364900 181956355 187155108 189383145 192659670 193472580 194750405 195775825 201369420 207076380 207292050 208166700 209541575 214066300 217430199 218347626 219268924 221867550 222803700 224769615 227259774 233700486 233943885 234686564 234930990 241589110 241840725 251449890 251711775 252510860 254738897 258845475 259937650 265136403 269723538 270547350 272650567 274086155 275228100 281917188 284976542 289906932 290208870 293358205 299692820 301739868 310614570 311925180 312250050 315638575 321099450 322454300 324656820 327521439 328903386 334205550 335615700 338224754 345127300 350550729 352029846 352396485 353515204 362383665 363912710 374616025 377174835 378766290 385319340 389500810 389906475 391551650 405821025 410701487 414584100 419083150 427464813 434860398 436695252 441894005 443735100 449539230 454519548 467400972 467887770 469861980 481649175 483178220 483681450 493355079 502899780 503423550 507337131 509477794 517690950 519875300 528044769 530272806 539447076 541094700 545301134 545869065 548172310 568149435 569953084 580417740 584251215 586716410 587327475 603972775 618651607 621229140 624500100 628624725 631277150 642198900 655042878 657806772 662151377 668411100 674308845 676449508 701101458 704059692 704792970 712441355 724767330 725522175 727825420 749232050 754349670 757532580 764216691 776536425 779001620 779812950 783103300 795409209 811642050 817951701 821402974 822258465 838166300 845561885 854929626 869720796 880074615 883788010 899078460 909781775 935775540 946915725 963298350 967362900 973752025 986710158 997417897 1006847100 1014674262 1018955588 1035381900 1056089538 1060545612 1087150995 1090602268 1091738130 1096344620 1123848075 1136298870 1168502430 1169719425 1173432820 1174654950 1183786639 1207945550 1232104461 1237303214 1257249450 1262554300 1273694485 1282394439 1310085756 1324302754 1325682015 1348617690 1363252835 1370430775 1402202916 1409585940 1424882710 1449534660 1451044350 1466791025 1498464100 1508699340 1522011393 1528433382 1553072850 1559625900 1590818418 1623284100 1635903402 1637607195 1642805948 1644516930 1691123770 1709859252 1752753645 1760149230 1761982425 1767576020 1811918325 1819563550 1855954821 1885874175 1893831450 1908553969 1926596700 1947504050 1973420316 1986454131 1994835794 2029348524 2053507435 2112179076 2137324065 2174301990 2183476260 2209470025 2247696150 2272597740 2292650073 2337004860 2339438850 2349309900 2367573278 2415891100 2453855103 2464208922 2466775395 2474606428 2514498900 2536685655 2547388970 2564788878 2640223845 2648605508 2651364030 2697235380 2726505670 2729345325 2740861550 2840747175 2849765420 2874910409 2902088700 2921256075 2933582050 2992253691 3044022786 3056866764 3093258035 3106145700 3181636836 3271806804 3275214390 3289033860 3310756885 3371544225 3382247540 3505507290 3520298460 3523964850 3551359917 3562206775 3623836650 3639127100 3696313383 3711909642 3771748350 3787662900 3817107938 3821083455 3895008100 3972908262 3977046045 3989671588 4089758505 4107014870 4111292325 4227809425 4274648130 4330561249 4348603980 4400373075 4418940050 4495392300 4585300146 4635059639 4678877700 4735146556 4907710206 4928417844 4933550790 4987089485 5073371310 5094777940 5129577756 5280447690 5302728060 5435754975 5453011340 5458690650 5481723100 5567864463 5681494350 5725661907 5749820818 5842512150 5867164100 5918933195 5959362393 5984507382 6088045572 6160522305 6186516070 6368472425 6411972195 6550428780 6621513770 6628410075 6743088450 6816264175 6981925279 7011014580 7047929700 7102719834 7124413550 7247673300 7392626766 7423819284 7543496700 7610056965 7634215876 7642166910 7945816524 7954092090 8179517010 8188035975 8214029740 8222584650 8455618850 8549296260 8624731227 8661122498 8763768225 8800746150 8837880100 8976761073 9170600292 9270119278 9279774105 9542769845 9815420412 9867101580 9932270655 9974178970 10146742620 10267537175 10560895380 10654079751 10686620325 10871509950 10917381300 11135728926 11256573409 11362988700 11451323814 11463250365 11499641636 11685024300 11837866390 11918724786 11969014764 12269275515 12321044610 12333876975 12373032140 12683428275 12736944850 12823944390 12991683747 13201119225 13243027540 13256820150 13359877783 13486176900 13632528350 13905178917 13963850558 14205439668 14248827100 14374552045 14785253532 14961268455 15220113930 15284333820 15466290175 15908184180 16359034020 16376071950 16445169300 16553784425 16911237700 17176985721 17249462454 17322244996 17527536450 17601492300 17756799585 17953522146 18481566915 18540238556 18559548210 19085539690 19105417275 19864541310 19885230225 19948357940 20124372863 20448792525 20535074350 20945775837 21308159502 21373240650 21652806245 21743019900 22271457852 22513146818 22902647628 22926500730 23175298195 23675732780 23837449572 24538551030 24642089220 24667753950 24935447425 25366856550 25473889700 25647888780 25874193681 25983367494 26402238450 26513640300 26719755566 27265056700 27810357834 27839322315 27927701116 28628309535 28749104090 29594665975 29796811965 29922536910 30440227860 30802611525 30932580350 32059860975 32445417473 32752143900 33107568850 33769720227 34353971442 34498924908 34909626395 35055072900 35513599170 35907044292 36963133830 37119096420 38050284825 38171079380 38210834550 38975051241 39729082620 39770460450 40079633349 40248745726 40897585050 41070148700 41715536751 41891551674 42616319004 42746481300 43123656135 43305612490 44883805365 45026293636 45853001460 46350596390 46398870525 47713849225 48873476953 49077102060 49335507900 49661353275 49870894850 50733713100 51748387362 51966734988 52804476900 53270398755 53439511132 55620715668 55678644630 56282867045 57256619070 57316251825 57498208180 59189331950 59593623930 59845073820 60373118589 61346377575 61605223050 61865160700 62837327511 64119721950 64890834946 64958418735 66215137700 66799388915 67539440454 68707942884 69525894585 69819252790 71027198340 71872760225 73926267660 74806342275 76100569650 76421669100 77950102482 78796013863 79540920900 80159266698 80497491452 81795170100 83431073502 83783103348 85884928605 86247312270 86611224980 88783997925 89767610730 92407834575 92701192780 92797741050 93519144481 95427698450 97336252419 97746953906 99322706550 99741789700 100621864315 101309160681 103496774724 104728879185 106540797510 108264031225 111357289260 112565734090 114513238140 114632503650 115876490975 118378663900 119187247860 120238900047 120746237178 122692755150 123210446100 125674655022 128239443900 129370968405 129781669892 129916837470 133598777830 135078880908 139051789170 139196611575 139638505580 143141547675 143745520450 146620430859 148984059825 149612684550 152201139300 155900204964 157592027726 160318533396 162227087365 166862147004 168848601135 171769857210 172494624540 174548131975 177567995850 179535221460 181119355767 184815669150 185595482100 187038288962 190855396900 194672504838 194875256205 195493907812 198645413100 200398166745 201243728630 202618321362 208577683755 209457758370 213081595020 215618280675 216528062450 224419026825 225131468180 227117922311 229265007300 231752981950 236388041589 240477800094 241492474356 244367384765 245385510300 251349310044 258741936810 259833674940 266351993775 267197555660 278103578340 278393223150 280557433443 281414335225 286283095350 287491040900 292008757257 293240861718 297968119650 299225369100 301865592945 314186637555 315184055452 324454174730 324792093675 333996944575 337697202270 342114338671 343539714420 347629472925 349096263950 355135991700 362238711534 369631338300 374076577924 389345009676 389750512410 393980069315 400796333490 402487457260 405236642724 417155367510 418915516740 429424643025 431236561350 433056124900 439861292577 448838053650 454235844622 463505963900 467595722405 472776083178 480955600188 486681262095 488734769530 503109321575 506545803405 517483873620 523644395925 532703987550 551572097041 556786446300 561114866886 562828670450 572566190700 584017514514 586481723436 595936239300 601194500235 603731185890 628373275110 646854842025 648908349460 649584187350 667993889150 675394404540 681353766933 684228677342 695258945850 698192527900 709164124767 724477423068 733102154295 779501024820 787960138630 801592666980 811135436825 834310735020 841672300329 844243005675 858849286050 862473122700 879722585154 897676107300 905596778835 908471689244 935191444810 945552166356 973362524190 974376281025 977469539060 1001990833725 1006218643150 1013091606810 1026343016013 1042888418775 1047288791850 1065407975100 1103144194082 1122229733772 1125657340900 1135589611555 1168035029028 1181940207945 1202389000470 1207462371780 1221836923825 1256746550220 1293709684050 1299168374700 1335987778300 1362707533866 1368457354684 1390517891700 1402787167215 1418328249534 1460043786285 1466204308590 1509327964725 1570933187775 1575920277260 1589825456177 1622270873650 1654716291123 1683344600658 1688486011350 1710571693355 1717698572100 1759445170308 1811193557670 1870382889620 1946725048380 1948752562050 1969900346575 2003981667450 2012437286300 2026183213620 2044061300799 2052686032026 2085776837550 2094577583700 2199306462885 2206288388164 2271179223110 2337978612025 2363880415890 2404778000940 2433406310475 2443673847650 2532729017025 2587419368100 2725415067732 2757860485205 2805574334430 2836656499068 2920087572570 2932408617180 3005972501175 3018655929450 3079029048039 3141866375550 3179650912354 3244541747300 3309432582246 3366689201316 3376972022700 3406768834665 3421143386710 3545820623835 3622387115340 3665510771475 3861004679287 3897505124100 3939800693150 4007963334900 4088122601598 4105372064052 4171553675100 4208361501645 4398612925770 4527983894175 4542358446220 4675957224050 4727760831780 4769476368531 4866812620950 4887347695300 4964148873369 5065458034050 5131715080065 5515720970410 5611148668860 5677948057775 5840175145140 5909701039725 6011945002350 6037311858900 6158058096078 6283732751100 6359301824708 6618865164492 6813537669330 6842286773420 7013935836075 7091641247670 7300218931425 7331021542950 7722009358574 7879601386300 7949127280885 8176245203196 8273581455615 8416723003290 8552858466775 8797225851540 9055967788350 9351914448100 9538952737062 9733625241900 9928297746738 10130916068100 10220306503995 10263430160130 10996532314425 11031441940820 11355896115550 11583014037861 11819402079450 12023890004700 12316116192156 13627075338660 13789302426025 14027871672150 14183282495340 14308429105593 14600437862850 14662043085900 15395145240195 15444018717148 15898254561770 16547162911230 16833446006580 17033844173325 17105716933550 17729103119175 18111935576700 19077905474124 19305023396435 19856595493476 20440613007990 20526860320260 21041807508225 21993064628850 22711792231100 23166028075722 23638804158900 23847381842655 24820744366845 25658575400325 27027032755009 27578604852050 28055743344300 28616858211186 29200875725700 30790290480390 31796509123540 33094325822460 34067688346650 34211433867100 34749042113583 35458206238350 38610046792870 39745636404425 40881226015980 41367907278075 42083615016450 43986129257700 46332056151444 47694763685310 49641488733690 51101532519975 51317150800650 54054065510018 55157209704100 57233716422372 57915070189305 61580580960780 68135376693300 69498084227166 70916412476700 71542145527965 76975726200975 77220093585740 79491272808850 81081098265027 82735814556150 84167230032900 95389527370620 96525116982175 99282977467380 102203065039950 102634301601300 108108131020036 115830140378610 119236909213275 124103721834225 135135163775045 138996168454332 143084291055930 153951452401950 158982545617700 162162196530054 165471629112300 173745210567915 193050233964350 204406130079900 231660280757220 238473818426550 243243294795081 248207443668450 270270327550090 286168582111860 289575350946525 307902904803900 324324393060108 347490421135830 357710727639825 386100467928700 405405491325135 476947636853100 486486589590162 496414887336900 540540655100180 579150701893050 675675818875225 694980842271660 715421455279650 810810982650270 868726052839575 972973179180324 1158301403786100 1216216473975405 1351351637750450 1430842910559300 1621621965300540 1737452105679150 2027027456625675 2432432947950810 2702703275500900 3474904211358300 4054054913251350 4864865895901620 6081082369877025 8108109826502700 12162164739754050 24324329479508100
- Sum of all divisors σ(n): 95696361153265327
- Sum of proper divisors (its aliquot sum) s(n): 71372031673757227
- 24324329479508100 is an abundant number, because the sum of its proper divisors (71372031673757227) is greater than itself. Its abundance is 47047702194249127
Bases of 24324329479508100
- Binary: 10101100110101011011001010010100000011010010000100001002
- Hexadecimal: 0x566AD94A069084
- Base-36: 6NI96P4IU10
Squares and roots of 24324329479508100
- 24324329479508100 squared (243243294795081002) is 591673004627666795057817965610000
- 24324329479508100 cubed (243243294795081003) is 14392049108693887895665650548872008525516441000000
-
24324329479508100 is a
perfect square number . Itssquare root is 155962590 -
The
cube root of 24324329479508100 is 289743.4492051679
Scales and comparisons
How big is 24324329479508100?- 24,324,329,479,508,100 seconds is equal to 773,438,437 years, 18 weeks, 4 days, 15 minutes.
-
To count from 1 to 24,324,329,479,508,100 would take you about two billion, three hundred twenty million, three hundred fifteen thousand, three hundred twelve years!
This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)
- A cube with a volume of 24324329479508100 cubic inches would be around 24145.3 feet tall.
Recreational maths with 24324329479508100
- 24324329479508100 backwards is 00180597492342342
- 24324329479508100 is a
Harshad number . - The number of decimal digits it has is: 17
- The sum of 24324329479508100's digits is 63
- More coming soon!
Link to this page
HTML: To link to this page, just copy and paste the link below into your blog, web page or email.
BBCODE: To link to this page in a forum post or comment box, just copy and paste the link code below:
Cite this page
MLA style:
"Number 24324329479508100 - Facts about the integer". Numbermatics.com. 2024. Web. 20 June 2024.
APA style:
Numbermatics. (2024). Number 24324329479508100 - Facts about the integer. Retrieved 20 June 2024, from https://numbermatics.com/n/24324329479508100/
Chicago style:
Numbermatics. 2024. "Number 24324329479508100 - Facts about the integer". https://numbermatics.com/n/24324329479508100/
The information we have on file for 24324329479508100 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!
Keywords: Divisors of 24324329479508100, math, Factors of 24324329479508100, curriculum, school, college, exams, university, Prime factorization of 24324329479508100, STEM, science, technology, engineering, physics, economics, calculator, twenty-four quadrillion, three hundred twenty-four trillion, three hundred twenty-nine billion, four hundred seventy-nine million, five hundred eight thousand, one hundred.